Question: Solve for $x$ : $4\sqrt{x} - 10 = 9\sqrt{x} + 7$
Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} - 10) - 4\sqrt{x} = (9\sqrt{x} + 7) - 4\sqrt{x}$ $-10 = 5\sqrt{x} + 7$ Subtract $7$ from both sides: $-10 - 7 = (5\sqrt{x} + 7) - 7$ $-17 = 5\sqrt{x}$ Divide both sides by $5$ $\frac{-17}{5} = \frac{5\sqrt{x}}{5}$ Simplify. $-\dfrac{17}{5} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.